Diamagnetic Response due to Localization in Chains of Connected Mesoscopic Rings

A dynamic response to a magnetic field of a chain of connected mesoscopic rings is considered. We show that the low frequency behavior corresponds to localization of the electrons along the chain and to diamagnetic dynamic currents inside rings. The magnetization density due to these currents does not vanish even in the limit of the infinitely long chain of strongly connected rings showing that this is a macroscopic effect. Being of a dynamic origin the currents can be destroyed by inelastic scattering but we find that their time of persistence is at low enough temperatures macroscopically large. Thus, this may yield a new contactless method of studying the localization.